Assuming that 5 is an irrational number, prove that 2 + 3 5 is an irrational number.

Given, 5 is an irrational number. We need to prove that 2 + 3 5 is an irrational number. Let 2 + 3 5 is not an irrational number ∴ it can be written in the form a b , where b ≠ 0 and a and b are coprime. So, 2 + 3 5 = a b Subtracting 2 from both sides 3 5 = a b - 2 5 = a - 2 b 3 b , this contradicts LHS is an irrational because 5 is an irrational (given) and RHS is a rational number. So, LHS = RHS is not possible. Hence, our assumption is wrong ∴ 2 + 3 5 is an irrational number

Assuming that 5 is an irrational number, prove that 2 + 3 5 is an irrational number.

Given, 5 is an irrational number. We need to prove that 2 + 3 5 is an irrational number. Let 2 + 3 5 is not an irrational number ∴ it can be written in the form a b , where b ≠ 0 and a and b are coprime. So, 2 + 3 5 = a b Subtracting 2 from both sides 3 5 = a b - 2 5 = a - 2 b 3 b , this contradicts LHS is an irrational because 5 is an irrational (given) and RHS is a rational number. So, LHS = RHS is not possible. Hence, our assumption is wrong ∴ 2 + 3 5 is an irrational number

Assuming that 5 is an irrational number, Prove that : 3 5 - 2 is also an irrational number.

Given, 5 is an irrational number. We need to prove that 3 5 - 2 is an irrational number. Let 3 5 - 2 is not an irrational number ∴ it can be written in the form a b , where b ≠ 0 and a and b are coprime. So, 3 5 - 2 = a b Adding 2 to both sides of the equation, 3 5 = a b + 2 5 = a + 2 b 3 b , this contradicts LHS is an irrational because 5 is an irrational (given) and RHS is a rational number. So, LHS = RHS is not possible. Hence, our assumption is wrong ∴ 3 5 - 2 is an irrational number

Assuming that 5 is an irrational number, Prove that : 3 5 - 2 is also an irrational number.

Given, 5 is an irrational number. We need to prove that 3 5 - 2 is an irrational number. Let 3 5 - 2 is not an irrational number ∴ it can be written in the form a b , where b ≠ 0 and a and b are coprime. So, 3 5 - 2 = a b Adding 2 to both sides of the equation, 3 5 = a b + 2 5 = a + 2 b 3 b , this contradicts LHS is an irrational because 5 is an irrational (given) and RHS is a rational number. So, LHS = RHS is not possible. Hence, our assumption is wrong ∴ 3 5 - 2 is an irrational number